The purpose of this paper is to study the method of approximation for a zero of the sum of two maximal monotone mappings in Banach spaces and prove strong convergence of the proposed method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

中文翻译：

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Banach空间中两个最大单调映射的和的零近似的强收敛定理

本文的目的是研究Banach空间中两个最大单调映射的和为零的逼近方法，并证明该方法在适当条件下的强收敛性。证明方法具有独立利益。另外，我们将一些应用程序应用于最小化问题。我们的定理改进并统一了针对这一重要类别的非线性映射已证明的大多数结果。